The person would not disclose the total value of the new offer, but the fact that the Yankees added a seventh year underscores just how desperate they are to sign the left-hander.

Yankees general manager Brian Cashman declined to comment on the new offer. “We’ll stay engaged with the agent until the player comes off the board,” Cashman said. “We’ve communicated what we’re comfortable doing.”

The Yankees were initially reluctant to offer more than six years for a 32-year-old pitcher, although the team is thought to have the capacity to offer more money than any other club. Despite rumors of other teams offering seven years, it was unclear whether the mystery offers truly existed.

“They have a great team,” Cashman said. “They’ve had two huge acquisitions. They’re loading up like they always do. This is even more significant than a typical Red Sox reload.”

Cashman was scheduled to leave the winter meetings late Thursday morning and return to New York on an afternoon flight. He met with Crawford and his agent over dinner Tuesday night but said he never made an offer. He said he was comfortable with the team’s current outfield of Curtis Granderson, Nick Swisher and Brett Gardner and didn’t need to splurge on Crawford.

“I have a certain amount of money to spend,” he said. “I’m going to be aggressive on areas of need, not areas that aren’t of need.”